$f(x)=7x+2$ $g(x)=\dfrac{x^2}{x-5}$ Write $(g\circ f)(x)$ as an expression in terms of $x$. $(g\circ f)(x)=$
First, let's write $(g\circ f)(x)$ as $g(f(x))$ Next, we write $f(x)$ as the input to function $g$. $g({f(x)})=\dfrac{({f(x)})^2}{({f(x)})-5}$ Since $f(x)=7x+2$, this becomes: $\begin{aligned} g({f(x)})&=\dfrac{({7x+2})^2}{({7x+2})-5}\\ \\ &=\dfrac{49x^2+28x+4}{7x-3}\\ \\ \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $(g\circ f)(x)=\dfrac{49x^2+28x+4}{7x-3}$